Research commissioned by messaging security firm Cloudmark shows 66% of UK mobile phone users have received spam text messages.
The figure rises to 75% among 18 to 24 year olds, said Cloudmark, whose survey questioned 2,150 people.
The types of mobile spam consumers are receiving go beyond simple nuisance messages to attacks designed to steal personal information or trick the consumer into spending money.
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Of respondents that had been victims of spam, nearly one in ten were targeted with phishing attacks encouraging them to disclose personal data.
In addition, 38% received a text containing a link to another site, while 45% received a text message that tried to trick them into calling a premium rate number.
Neil Cook, head of technology EMEA at Cloudmark, said, "It's a fallacy to think that mobile messaging spam isn't yet an issue in the UK.
"Not only is it already a problem, but when you see three quarters of young people are subjected to mobile spam, the scale of the challenge comes into sharp focus."